EP3097614B1 - Dual-frequency optical source - Google Patents

Dual-frequency optical source Download PDF

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Publication number
EP3097614B1
EP3097614B1 EP15783006.8A EP15783006A EP3097614B1 EP 3097614 B1 EP3097614 B1 EP 3097614B1 EP 15783006 A EP15783006 A EP 15783006A EP 3097614 B1 EP3097614 B1 EP 3097614B1
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Prior art keywords
frequency
optical
dual
fiber
resonator
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German (de)
English (en)
French (fr)
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EP3097614A4 (en
EP3097614A2 (en
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Kerry Vahala
Jiang Li
Scott DIDDAMS
Xu Yi
Hansuek Lee
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California Institute of Technology CalTech
National Institute of Standards and Technology (NIST)
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California Institute of Technology CalTech
National Institute of Standards and Technology (NIST)
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/50—Transmitters
    • H04B10/501—Structural aspects
    • H04B10/503—Laser transmitters
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03B—GENERATION OF OSCILLATIONS, DIRECTLY OR BY FREQUENCY-CHANGING, BY CIRCUITS EMPLOYING ACTIVE ELEMENTS WHICH OPERATE IN A NON-SWITCHING MANNER; GENERATION OF NOISE BY SUCH CIRCUITS
    • H03B17/00—Generation of oscillations using radiation source and detector, e.g. with interposed variable obturator
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03L—AUTOMATIC CONTROL, STARTING, SYNCHRONISATION OR STABILISATION OF GENERATORS OF ELECTRONIC OSCILLATIONS OR PULSES
    • H03L7/00—Automatic control of frequency or phase; Synchronisation
    • H03L7/06—Automatic control of frequency or phase; Synchronisation using a reference signal applied to a frequency- or phase-locked loop
    • H03L7/08—Details of the phase-locked loop
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03L—AUTOMATIC CONTROL, STARTING, SYNCHRONISATION OR STABILISATION OF GENERATORS OF ELECTRONIC OSCILLATIONS OR PULSES
    • H03L7/00—Automatic control of frequency or phase; Synchronisation
    • H03L7/06—Automatic control of frequency or phase; Synchronisation using a reference signal applied to a frequency- or phase-locked loop
    • H03L7/16—Indirect frequency synthesis, i.e. generating a desired one of a number of predetermined frequencies using a frequency- or phase-locked loop
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/25—Arrangements specific to fibre transmission
    • H04B10/2507—Arrangements specific to fibre transmission for the reduction or elimination of distortion or dispersion
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/25—Arrangements specific to fibre transmission
    • H04B10/2575—Radio-over-fibre, e.g. radio frequency signal modulated onto an optical carrier
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/25—Arrangements specific to fibre transmission
    • H04B10/2589—Bidirectional transmission
    • H04B10/25891—Transmission components
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L7/00—Arrangements for synchronising receiver with transmitter
    • H04L7/0075—Arrangements for synchronising receiver with transmitter with photonic or optical means
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L7/00—Arrangements for synchronising receiver with transmitter
    • H04L7/0091—Transmitter details
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B2210/00—Indexing scheme relating to optical transmission systems
    • H04B2210/006—Devices for generating or processing an RF signal by optical means

Definitions

  • the field of the present invention relates to generating dual optical-frequency signals and dual-frequency optical sources.
  • apparatus and methods are described herein for generating dual optical-frequency signals exhibiting enhanced difference-frequency stability and reduced phase noise.
  • a dual-frequency optical source comprises: (a) first and second pump laser sources arranged to generate optical pump power at respective first and second pump laser frequencies v pump1 and v pump2 ; and (b) an optical resonator characterized by a Brillouin shift frequency v B and a free spectral range that is substantially equal to an integer submultiple of the Brillouin shift frequency.
  • Each one of the first and second pump laser sources is frequency-locked to a corresponding resonant optical mode of the optical resonator.
  • An output difference frequency v 2 -v 1 is greater than about 300 GHz.
  • the fiber optical resonator comprises an optical fiber greater than or equal to about 100 meters in length
  • a method for generating first and second optical output signals comprises simultaneously pumping the optical resonator with optical pump power from the first and second pump laser sources.
  • Microwave- and radio-frequency oscillators are widely used in communications, remote sensing, navigation, radar, scientific measurements, computers, clocks, time standards, and in other areas. They provide a single electrical frequency that can often be controllably tuned. Their performance is characterized using various metrics including power output, frequency tuning range, and frequency stability. The last of these metrics, frequency stability, is crucial to most applications, and the cost of an oscillator is directly related to the level of frequency stability that it provides. The very highest performance oscillators have typically been based on electrical oscillators that employ high-Q dielectric resonators to create a highly stable frequency.
  • Optical detection of two highly coherent laser signals is another well-known approach to generate a stable radio-frequency or microwave-frequency signal; two optical signals coincident on an optical detector (i.e., a photodetector) and having a frequency difference within the detection frequency bandwidth of the optical detector produce an electrical output signal from the optical detector at the optical difference frequency of the optical signals, also referred to as a beat note or a beat frequency.
  • an optical detector i.e., a photodetector
  • a newer approach developed over the last few years employs a revolutionary, all-optical approach to microwave synthesis using a device known as a frequency-comb optical divider (or simply "optical divider").
  • Optical dividers accept as an input a highly coherent optical signal that oscillates at 100s of THz.
  • This very high input frequency is divided down to a rate in the radio-frequency or microwave-frequency range (100s of MHz or 100s of GHz) using the optical divider.
  • This division process is accompanied by a dramatic reduction of the phase noise in the final signal relative to the initial optical signal thereby endowing the radio/microwave signal with remarkable (and record) stability.
  • the frequency-comb optical divider employs a special mode locked laser to achieve this reduction.
  • a microwave-frequency signal provided by an electrical oscillator having a frequency control input (sometimes called a voltage-controlled oscillator, or VCO).
  • VCO voltage-controlled oscillator
  • This novel approach is described herein along with preliminary measurements that demonstrate the feasibility of the method.
  • two reference optical signals, provided by lasers are frequency-stabilized so that the relative frequency of the lasers (i.e., their difference frequency) is as stable as possible (or practicable to achieve performance necessary for a given use or application, i . e ., relatively stabilized within an operationally acceptable reference bandwidth).
  • the laser signals are then phase modulated using a cascade of phase modulators that are driven by the VCO.
  • phase-modulated optical signals can be spectrally broadened to further increase number of sidebands in the side-band frequency spectrum, using an intensity modulator, a dispersion compensator, an optical amplifier (if needed or desired), and a nonlinear optical medium. It is desirable for the frequency separation of the lasers be as large as practicable (for a given use or application) to provide the maximum practicable stabilization of the VCO. However, the frequency separation cannot exceed the range of sidebands generated by the phase modulation cascade (and nonlinear optical broadening, if employed). The two innermost sidebands (see Fig.
  • the photodiode signal contains phase information arising from the VCO and is used to stabilize the VCO.
  • the inventive method has already enabled generation of highly stable microwave-frequency signals having a phase noise level well below a high performance electrical oscillator at offset frequencies of 10kHz and 100kHz.
  • the performance of the inventive method can be substantially improved by further increasing the frequency separation of the two reference optical signals.
  • these reference optical signals are provided by dual pumping of a single high-Q disk resonator to produce stimulated Brillouin oscillation at two distinct wavelengths. The frequency separation is limited by the ability to pump separate lines efficiently within the same cavity, as is discussed further below.
  • Other dual optical-frequency reference sources can be employed, e.g., a reference source comprising two lasers frequency-locked to separate modes of a single reference resonator cavity.
  • the inventive method disclosed herein has not yet attained the same, record frequency stability.
  • improvements in pulse-broadening methods described above should result in performance improvements beyond those already demonstrated, since phase noise is reduced by the square of the division ratio and larger difference frequency results in a larger division ratio.
  • the inventive approach does not require a mode-locked frequency comb generator, which is a sophisticated and costly device. Instead, the inventive method employs relatively simpler and less costly optical components, most of which are available commercially.
  • the reference frequency i.e., the difference frequency of two optical sources
  • the reference frequency depends on the relative stability of two resonances within a single resonator.
  • the conventional frequency-comb divider approach relies upon optical detection of a train of high peak power pulses of light with high bandwidth.
  • the linearity of the photodetection process has been shown to be crucial to attaining frequency stability using this approach and greatly restricts the types of optical detectors that may be employed.
  • the present invention can employ lower-bandwidth optical detectors or detectors with relaxed linearity requirements.
  • inventive apparatus and methods disclosed herein for achieving optical frequency division for high-performance microwave-frequency signal generation employ cascaded phase modulation comprising direct phase modulation and also self-phase modulation (if needed or desired to achieve larger division ratios than can be achieve using direct phase modulation alone).
  • cascaded phase modulators do not have an intrinsic repetition frequency since there is no optical cavity. While this can endow the cascade-generated comb of sidebands with an arbitrarily chosen line spacing frequency, it also means that optical frequency division must be accomplished in a fashion different from that used with conventional frequency combs.
  • Figs. 1-3 illustrate the inventive approach in which two laser lines having sufficiently good (i.e., operationally acceptable) relative frequency stability provide two optical reference signals 120a/120b (characterized by spectrum 101) for the microwave-frequency source.
  • Fig. 1 is a high-level block diagram of the system;
  • Fig. 2 includes further details of certain elements of the system;
  • Fig. 3 is a schematic representation of the frequency spectrum of the optical signals relevant to the inventive approach.
  • the two laser lines 120a/120b are produced by concomitant Brillouin oscillation in a single high-Q microcavity 110 or fiber-loop cavity 110' (FLC) pumped by two corresponding, independent pump lasers 130a/130b ( Figs. 7 and 8 , discussed further below).
  • the two laser lines 120a/120b could also be produced by a dual-mode laser, by frequency-locking two lasers to distinct optical modes of a single, common reference cavity 180, or by frequency-locking to distinct atomic transitions 190.
  • the two reference laser lines enter the electro-optic frequency divider (i.e., an electro-optic sideband generator) where they are phase modulated by a pair of modulators 220 at a frequency f M set by a voltage-controlled electrical oscillator 600 (VCO).
  • VCO voltage-controlled electrical oscillator 600
  • the sideband spectrum 301 created by the phase modulators 220 can be further broadened by pulse-forming and self-phase phase modulation in an optical fiber 350.
  • the multiple sideband optical signals thus formed extend from each laser line 120a/120b and results in a pair of sidebands optical signals 430a/430b (typically near the mid-point of the difference frequency span; see spectrum 401).
  • the sideband optical signals 430a/430b are optically filtered and detected using a photodiode 420.
  • the beat note signal generated by the two detected sideband signals 430a/430b contains the phase noise of the VCO 600 magnified by the optical division factor ( N 1 + N 2 ), the number of sidebands needed to get to the sidebands signals 430a/430b).
  • the beat note therefore provides a suitable error signal for phase-lock-loop control of the VCO 600.
  • the inventive microwave-frequency source with a more conventional microwave-frequency source employing a frequency reference 10 and a VCO 30.
  • the VCO 30 provides the highest frequency in the system. It is stabilized by electrical frequency division 20 and phase comparison to a lower-frequency reference oscillator 10, such as a quartz oscillator.
  • the inventive electro-optic frequency divider disclosed herein operates by reversing the positions of the reference and the VCO in the frequency domain.
  • the reference 100 is provided by the relative frequency separation of the laser lines; that frequency separation is made many times greater than the frequency of the VCO 600 (in the present implementation this typically is a non-detectable rate using an optical detector).
  • the reference frequency is divided down to the VCO frequency (in the inventive source) as opposed to dividing the VCO frequency down to the reference frequency rate (as in the conventional source).
  • the inventive device benefits from (i) the stability of optical oscillators, which now typically exceeds that of microwave oscillators, and (ii) the power of optical frequency division to transfer the stability to the microwave domain.
  • the inventive divider derives its rate from the electrical VCO 600, it is continuously tunable.
  • the frequency output is set by the tuning range of the electrical VCO and the frequency separation of the reference laser lines and not fixed by a cavity repetition rate.
  • Fig. 3 illustrates the origin of the phase noise reduction provided by the inventive frequency divider.
  • the accumulated phase noise contributions in the generated sideband optical signals are tracked from the two laser sources to the phase difference of the detected sidebands generating the detectable beat note.
  • the detected beat note is compared to a reference oscillator signal.
  • ⁇ the phase of the VCO 600 to nullify the phase difference, ⁇
  • the ultimate lower limit of the relative phase noise of the VCO 600 is given by the optical phase noise of the laser lines reduced by the division factor squared ( i.e., reduced by a factor of ( N 1 + N 2 ) 2 ) .
  • the laser frequency separation i.e., difference frequency
  • this magnitude of the difference frequency is determined by the span of the dual-pumped Brillouin lasers.
  • the optical reference laser signals 120a/120b are provided by Brillouin laser lines co-lasing within a single silica-on-silicon high-Q disk resonator 110.
  • the coherence properties of the individual Brillouin laser lines is excellent, and the relative frequency stability of the Brillouin laser lines is enhanced by co-lasing within a common resonator.
  • the Brillouin laser lines are separated by a difference frequency sufficiently large that a dual pump configuration is needed.
  • the silica disk resonator 110 is designed and fabricated with a free-spectral-range (FSR) of about 10.890 GHz that substantially matches the Brillouin shift frequency in silica at a pump wavelength of 1550 nm.
  • FSR free-spectral-range
  • Other needed, desired, or suitable materials can be employed that exhibit different Brillouin shift frequencies.
  • Each pump laser 130a/130b (emitting at corresponding wavelengths ⁇ 1 and ⁇ 2 ) is frequency-locked to a corresponding distinct resonant optical mode of the disk resonator 110 using the Pound-Drever-Hall (PDH) technique, is coupled into the disk resonator 110 through a circulator 114, and excites its own corresponding Brillouin laser in the backward-propagating direction at respective optical reference frequencies v 1 and v 2 .
  • PDH Pound-Drever-Hall
  • the PDH technique is implemented for each pump laser 130a/130b by employing respective optical bandpass filters 132a/132b, photodetectors 134a/134b, and feedback/servo mechanisms 136a/136b; control of each pump wavelength can be via direct laser control (as with pump laser 130a) or via frequency shifting of the laser output (as with acousto-optic shifting of the output of pump laser 130b).
  • the frequency separation i.e., the difference frequency v 2 -v 1
  • Fig. 8 shows a similar example wherein the disk resonator 110 has been replaced by a fiber-loop optical resonator 110' (i.e., a fiber-loop cavity or FLC).
  • Dual pumping of fiber-based SBS lasers in a single, common FLC previously has been applied to generate stable microwave-frequency signals by conventional optical detection of the optical signals, with the two pump laser wavelengths being the sidebands of a single continuous-wave (CW) laser generated by electro-optic phase modulation at the desired microwave frequency.
  • the two SBS laser frequencies are by necessity sufficiently close in frequency that their difference frequency (i.e., beat note) is directly detectable using an optical detector.
  • the SBS laser frequencies v 2 and v 1 are separated at much larger frequency separations (e.g., 109, 198, 327, and 1612 GHz in various experiments, by dual pumping on disk resonator optical modes separated by 10, 18, 30 and 148 cavity FSR using independently tunable CW lasers).
  • These increasing frequency separations increase the phase noise reduction by optical frequency division by increasing division factors; it is therefore desirable that the frequency separation (i.e., the difference frequency v 2 -v 1 ) be made as large as possible or practicable.
  • Such large frequency separations are typically so large that it is not possible to optically detect the difference frequency (i.e., the beat note) because it greatly exceeds the detection bandwidth of optical detectors.
  • the maximum separation of 1612 GHz in embodiments constructed thus far is limited by one of the SBS pump lasers being at 1537 nm, near the edge of the gain bandwidth of the erbium-doped fiber amplifier employed; other pump sources can be employed to achieve greater spectral separation of the optical reference signals 120a/120b. Measured optical spectra of the dual SBS lines at some of these spectral separations is shown in Fig. 5A . It is worth noting that the two SBS laser signals 120a/120b share not only the single, common chip-based disk resonator 110, but also the same fiber-optic pathway throughout the subsequent optical/electrical conversion, thereby suppressing path length variation effects.
  • the optical reference signals 120a/120b are coupled to the optical divider section using a circulator 114.
  • the sideband generator 200 is employed that comprises two phase modulators 220/230 with relatively low V ⁇ ⁇ 3.9V (at 12 GHz) are cascaded and phase synchronized with corresponding RF phase shifters 224/234 ( Figs. 1 and 2 ).
  • the phase modulators 220/230 are driven at 32.5 dBm and 30.7 dBm, corresponding to a total phase modulation amplitude up to about 6 ⁇ ( ⁇ ⁇ V drive /V ⁇ ), which is also approximately equal to half of the number of sidebands produced by the modulators 220/230.
  • the drive signal to the phase modulators 220/230 i.e., the sideband generator input electrical signal
  • the drive signal to the phase modulators 220/230 is a portion 620 of the output electrical signal of the VCO 600 at a frequency f M (acting as a sideband generator input optical signal).
  • EOM sidebands i.e., N 1 + N 2 up to about 30
  • EOM sidebands can be generated using only a first portion 200 of the sideband generator (i.e., using only phase modulators 220/230 for generating the sideband signals 310; path I in Fig. 2 ), resulting in a difference frequency v 2 -v 1 of up to about 327 GHz and optical division by a factor of up to about 30.
  • a measured optical spectrum showing both the original SBS laser lines (18 FSR frequency separation) and the resulting phase modulation sidebands is shown in Fig. 5B .
  • phase noise of the microwave-frequency signal 610 will be reduced by about a factor of about 900, relative to phase noise of the difference frequency of the optical reference signals 120a/120b, by feedback stabilization of the frequency f M (described further below).
  • Two phase modulators are employed in the example shown in Fig. 2 ; however, a single phase modulator can be employed if it provides sufficiently large modulation to produce sufficiently many sidebands.
  • phase modulators can be used, or phase modulators providing larger phase modulation amplitude can be used.
  • so-called continuum generation e.g ., as described in the publications of Huang et al (2008), Morohashi et al (2009), Ishizawa et al (2013, and Suzuki et al (2013), referred to above
  • path II in Fig. 2 can be employed by employing a second portion 300 of the sideband generator.
  • That portion comprises an intensity modulator 320 (driven at frequency f M by a portion of the VCO signal 620 and synchronized using a phase shifter 324), a dispersion compensator 330, an optical amplifier 340, and a nonlinear optical medium 350.
  • the intensity modulator 320 can comprise an electro-optic Mach-Zehnder interferometer
  • the dispersion compensator 330 can comprise a suitable length of suitably dispersive optical fiber (e.g., dispersion-shifted optical fiber or an optical fiber including a dispersion-shifting grating)
  • the optical amplifier 340 can comprise an erbium-doped optical fiber amplifier (EDFA)
  • the nonlinear optical medium 350 can comprise a suitable length of highly nonlinear optical fiber (HNLF).
  • HNLF highly nonlinear optical fiber
  • Other functionally equivalent components can be employed, e.g., an electroabsorption modulator.
  • continuum generation cascaded with the phase modulators 220/230, can generate sufficiently many sidebands to enable the two reference optical signals 120a/120b to be spaced farther apart spectrally than is typically possible using phase modulators alone; in this example, a difference frequency v 2 -v 1 can be generated up to 148 FSR of the disk resonator 110 ( i.e., up to about 1.6 THz apart in this example; N 1 + N 2 up to 148; limited by the gain bandwidth of the EDFA, as noted above).
  • phase noise of the microwave-frequency signal 610 will be reduced by about a factor of over 20,000 relative to phase noise of the optical reference signals 120a/120b by feedback stabilization of the frequency f M (described further below). Even greater reduction of phase noise can be achieved by using even larger difference frequencies
  • a reference oscillator 510 generates a reference oscillator electrical signal at frequency f R (a quartz oscillator operating at about 10 MHz in this example; any suitable reference oscillator can be employed; frequencies f R from about 1 MHz to about 500 MHz have been employed).
  • the phase noise contributed by the reference oscillator 510 is also reduced by the overall frequency division and does not present any limit on the phase noise reduction achievable by the optical frequency division process.
  • An electrical circuit 520 compares the phases of the photodiode and reference electrical signals and generates an error signal (in any needed, desired, or suitable way), which is then loop-filtered by the circuit 520 (in any needed, desired, or suitable way).
  • the loop-filtered error signal serves as a VCO electrical input signal 530 used for phase-locking the VCO 600 to a subharmonic (i.e., integer submultiple) of the frequency v 2 -v 1 ⁇ f R .
  • the VCO comprises a microwave generator operated using the external FM modulation input mode; any suitable type or implementation of a VCO can be employed.
  • the uppermost curve in Fig. 5C gives the single sideband (SSB) phase noise (L ⁇ ) of the beat note produced by optical detection of output of the example dual SBS lasers of Fig. 7 on a fast optical detector (50 GHz bandwidth).
  • SSB single sideband
  • L ⁇ phase noise
  • the dual SBS laser signals are pumped at three FSR apart, resulting in a beat note at 32.7 GHz that is both detectable using an optical detector and can be analyzed by an electrical phase noise analyzer.
  • the phase noise level has been shown to remain approximately constant with frequency tuning of the SBS laser frequencies and therefore provides a measure of the reference phase noise of the lasers even when they are tuned to very large (i.e., non-detectable) frequency separations used in the invention frequency division process.
  • the noise spectrum is limited by Schawlow-Townes noise, while at offset frequencies less than 100Hz a technical noise component is present.
  • this spectrum provides the reference noise level (invariant of frequency difference) that is reduced quadratically by the optical frequency division factor N 1 + N 2 .
  • the VCO 600 is locked to the divided optical reference as shown in Figs.
  • Fig. 5C are the corresponding measured phase noise spectra of the VCO 600 at 10.89 GHz when optically dividing by 30 times (second lowest curve) and 148 times (lowest curve) relative to the initial frequency separation of the dual SBS lines 120a/120b. Decrease of the phase noise with the increase of the division ratio is clearly shown by the data.
  • the frequency of the output signal 610 is held at 10.89 GHz in these measurements by adjusting the frequency separation of the Brillouin laser lines using the tunable pump laser sources 130a/130b.
  • the features in the phase noise spectra at around 900 kHz (division ratio of 30 achieved using path I in Fig. 2 ) and 300 kHz (division ratio of 148 achieved using path II in Fig. 2 ) are the servo bumps in the phase-locked loop control circuitry. Those frequencies are determined by the servo loop delay, which includes optical and electrical path lengths and the tuning response of the VCO 600.
  • the dashed curve in Fig. 5C is the phase noise spectrum of the free running VCO 600.
  • a phase noise reduction of around 20 dB for offset frequencies between 1 kHz and 100 kHz relative to the original free running VCO 600 is observed, and a phase noise level of -112 dBc/Hz at 10 kHz offset frequency and -127 dBc/Hz at 100 kHz offset frequency is achieved for the 10.89 GHz carrier.
  • the achieved phase noise level for the 10.89 GHz carrier is -104 dBc/Hz at 1 kHz offset frequency, -121 dBc/Hz at 10 kHz offset frequency, and -119 dBc/Hz at 100 kHz offset frequency.
  • the rise of the phase noise at 100 kHz offset for 148 division ratio is because this offset is close to the servo peak at 300 kHz (servo bandwidth).
  • Fig. 5D shows the measured spectra of the VCO output 610 at 10.89 GHz (20 kHz span and 30 Hz resolution bandwidth settings on the electrical spectrum analyzer).
  • the uppermost curve is the free running VCO spectrum, while the other spectra are, in descending order, the spectra of the phase-locked VCO 600 when dividing down 18, 30 and 148 times, respectively, from corresponding SBS frequency separations of 196, 327 GHz and 1.61 THz.
  • Fig. 5E summarizes these results by giving the measured phase noise at 1 kHz, 10 kHz and 100 kHz offset frequencies plotted versus division ratios of 1, 3, 4, 10, 18, 30 and 148.
  • the dashed lines give the 1/( N 1 + N 2 ) 2 fits and are in good agreement with the measured values.
  • the upper horizontal dashed line is the phase noise of an Agilent MXG microwave synthesizer (carrier 11 GHz, offset 100 kHz, Agilent online data sheet, Literature number 5989-7572EN), and the lower horizontal dashed line is the phase noise of a high performance Agilent PSG microwave synthesizer (carrier 11 GHz, offset 100 kHz, Agilent online data Sheet, Literature number 5989-0698EN, option UNX).
  • the microwave frequency f M has been fixed; however, that frequency can be adjusted by varying the division ratio.
  • the division ratio N 1 + N 2 and VCO frequency f M for a fixed separation of the dual SBS lines v 2 - v 1 .
  • the sideband frequencies nearly overlap at the midpoint for two different division ratios 26 and 30.
  • the only requirement is for the difference frequency v 2 -v 1 to be approximately equal to an integer multiple of the desired output/modulation frequency f M .
  • FIG. 6B shows the measured noise spectrum of a phase-locked 12.566 GHz output signal 610
  • Fig. 6C shows the measured noise spectrum of an output signal 610 at 9.075 GHz.
  • the initial reference frequency separation v 2 -v 1 also can be tuned.
  • Employing multiple reference cavities 110 or 180 having varying FSRs enables a wide range of output frequencies can be generated using a single divider.
  • a microwave-frequency source is arranged for generating an output electrical signal at an output frequency f M , and comprises: (a) a dual optical-frequency reference source 100; (b) an electro-optic sideband generator 200/300; (c) an optical bandpass filter 410; (d) an optical detector 420; (e) a reference oscillator 510; (f) an electrical circuit 520; and (g) a voltage-controlled electrical oscillator 600.
  • the dual optical-frequency reference source 100 is arranged so as to generate (i) a first optical reference signal 120a at a first optical reference frequency v 1 and (ii) a second optical reference signal 120b at a second optical reference frequency v 2 > v 1 .
  • An example of a spectrum 101 of the first and second optical reference signals 120a/120b is represented schematically in an inset of Fig. 1 .
  • the electro-optic sideband generator 200/300 is arranged so as to (i) receive the first and second optical reference signals 120a/120b and a sideband generator input electrical signal at the frequency f M and (ii) generate therefrom multiple sideband optical signals 210/310 at respective sideband optical frequencies of the form v 1 ⁇ n 1 f M and v 2 ⁇ n 2 f M , wherein n 1 and n 2 are integers.
  • An example of a spectrum 301 of the multiple sideband optical signals 310 is represented schematically in an inset of Fig. 1 and also in Fig. 3 .
  • the optical bandpass filter 410 is arranged so as to transmit a subset of the multiple sideband optical signals 210/310 including the sideband optical signal 430a at a frequency v 1 + N 1 f M and the sideband optical signal 430b at a frequency v 2 -N 2 f M (separated by ⁇ f , that typically is ⁇ f M ).
  • An example of a spectrum 401 of the transmitted sideband optical signals 430a/430b is represented schematically in an inset of Fig. 1 and also in Fig. 3 .
  • the reference oscillator 510 is arranged so as to generate a reference oscillator electrical signal at a reference oscillator frequency f R .
  • the electrical circuit 520 is arranged so as to (i) receive the optical detector electrical signal 440 and the reference oscillator electrical signal, (ii) generate therefrom, using a comparator portion of the electrical circuit 520, an electrical error signal dependent on relative phase of the optical detector and reference oscillator electrical signals, and (iii) process the electrical error signal using a loop-filter portion of the electrical circuit 520.
  • the voltage-controlled electrical oscillator 600 is arranged so as to (i) receive the loop-filtered electrical error signal 530 as a VCO input electrical signal and (ii) generate a VCO output electrical signal at the frequency f M , wherein a first portion 620 of the VCO output electrical signal is received by the electro-optic sideband generator 200/300 as the sideband generator input electrical signal and a second portion 610 of the VCO output electrical signal forms the output electrical signal of the microwave-frequency source.
  • Reception of the first portion 620 of the VCO output electrical signal by the electro-optic sideband generator 200/300 as the sideband generator input electrical signal results in the electrical circuit 520 and the voltage-controlled oscillator 600 being coupled in a negative feedback arrangement so as to function as a phase-locked loop (PLL).
  • Comparator and loop-filter portions of the electrical circuit 520 can be implemented in any needed, desired, or suitable way.
  • a method for generating the microwave-frequency output electrical signal 610 at the output frequency f M comprises: (a) generating the first and second optical reference signals 120a/120b using the dual optical-frequency reference source 100; (b) generating the multiple sideband optical signals 210/310 using the electro-optic sideband generator 200/300; (c) transmitting the sideband optical signals 430a/430b using the optical bandpass filter 420; (d) generating the optical detector electrical signal 440 using an optical detector 420; (e) generating the reference oscillator electrical signal using the reference oscillator 510; (f) generating the loop-filtered electrical error signal 530 using the electrical circuit 520; and (g) using the voltage-controlled electrical oscillator 600 to generate the VCO output electrical signal 610/620.
  • Reception of the first portion 620 of the VCO output electrical signal by the electro-optic sideband generator 200/300 as the sideband generator input electrical signal results in the electrical circuit 520 and the voltage-controlled oscillator 600 being coupled in a negative feedback arrangement so as to function as a phase-locked loop.
  • the output frequency f M can lie anywhere within the so-called microwave portion of the electromagnetic spectrum, e.g., between about 0.3 GHz and about 300 GHz. In some examples the output frequency f M is between about 1 GHz and about 100 GHz.
  • the electro-optic sideband generator 200/300 acts to divide the difference frequency v 2 -v 1 by a factor of N 1 + N 2 , resulting in a pair of sidebands optical signals 430a/430b (at respective frequencies v 1 + N 1 f M and v 2 -N 2 f M ) that are spectrally close enough together to both fall within the passband of the optical bandpass filter 410.
  • the electro-optic sideband generator 200/300 can therefore be referred to as an electro-optic frequency divider (EOFD).
  • EOFD electro-optic frequency divider
  • the reference difference frequency v 2 -v 1 is greater than about 100 GHz. In some of those examples, the reference difference frequency v 2 -v 1 is greater than about 1 THz, greater than 10 THz, or greater than 100 THz. Still larger reference difference frequencies can be employed as needed, desired, or suitable, or as suitable optical sources are developed or become available.
  • any suitable division ratio N 1 + N 2 can be employed.
  • the division ratio N 1 + N 2 is greater than or equal to 10, greater than or equal to 50, greater than or equal to 100, or greater than or equal to 1000.
  • a greater division ratio provides greater reduction of phase noise.
  • the reference optical signals 120a/120b can be provided at any needed, desired, or suitable optical frequencies.
  • first and second optical reference frequencies v 1 and v 2 are each between about 75 THz and about 750 THz (i.e., wavelengths between about 400 nm and about 4 ⁇ m), between about 120 THz and about 430 THz ( i.e., wavelengths between about 700 nm and about 2.5 ⁇ m), or between about 150 THz and about 300 THz ( i.e., between about 1 ⁇ m and about 2 ⁇ m).
  • the latter two ranges can be convenient due to ready availability of fiber-optic and/or solid state sources in those wavelength regions.
  • Other wavelengths can be employed.
  • the reference oscillator frequency and the beat frequency can be between about 1 MHz and about 500 MHz, between about 5 MHz and about 100 MHz, or between about 10 MHz and about 50 MHz.
  • the reference oscillator 510 comprises a crystal oscillator, e.g., a quartz oscillator.
  • the reference oscillator 510 comprises an electrical oscillator, e.g., a frequency-synthesized oscillator. Any suitably stable reference oscillator can be employed that provides sufficiently stable ( i.e., operationally acceptable) performance of the microwave-frequency source in a given use or application.
  • the dual optical-frequency reference source 100 is stabilized so as to maintain fluctuations of a reference difference frequency v 2 -v 1 (i.e., relative frequency stability of the lasers) within an operationally acceptable optical reference bandwidth.
  • the operationally acceptable reference bandwidth (given as a bandwidth characterized over a given time interval) is less than about 100 Hz over about a 1 second timescale, or less than about 1 Hz over about a 1 second timescale.
  • the operationally acceptable reference bandwidth (given as optical phase noise at a given offset frequency relative to the optical carrier frequency) is about -40dBc/Hz at 100Hz offset frequency and about -80dBc/Hz at 10kHz offset frequency, or about -80dBc/Hz at 100Hz offset frequency and about -125 dBc/Hz at 10kHz offset frequency.
  • improved levels of relative stability of the laser sources will translate directly into improvements in the overall frequency stability of the microwave-frequency output signal.
  • Still better stabilized references can be employed as needed, desired, or suitable, or as suitable optical sources are developed or become available.
  • the dual optical-frequency reference source 100 comprises first and second pump laser sources 130a/130b and an optical resonator 110 (a disk resonator; Fig. 7 ) or 110' (a fiber-loop resonator; Fig. 8 ).
  • the free spectral range (FSR) of the optical resonator 110/110' is substantially equal to an integer submultiple of a Brillouin shift frequency of the optical resonator.
  • the optical resonator comprises silica and the Brillouin shift frequency of the optical resonator is about 10.9 GHz; other needed, desired, or suitable materials can be employed that exhibit different Brillouin shift frequencies.
  • Each one of the first and second pump laser sources 120a/120b is frequency-locked to a corresponding resonant optical mode of the optical resonator 110/110'.
  • the first and second optical reference signals 120a/120b comprise stimulated Brillouin laser (SBL) output generated by optical pumping of the optical resonator simultaneously by the first and second pump laser sources 130a/130b, respectively.
  • SBL stimulated Brillouin laser
  • the free spectral range of the optical resonator 110/110' is substantially equal to the Brillouin shift frequency of the optical resonator.
  • the optical resonator comprises a ring optical resonator such as a disk optical resonator 110 (as in Fig. 7 ).
  • the optical resonator comprises a fiber optical resonator, such as a fiber-loop optical resonator 110' (as in Fig. 8 ) or a linear, Fabry-Perot-type fiber optical resonator (which can include, e.g., fiber Bragg gratings at the pump frequency or the SBL frequency).
  • each one of the first and second pump laser sources is frequency-locked to the corresponding resonant optical mode of the resonator 110/110' by a Pound-Drever-Hall mechanism; any suitable mechanism can be employed, e.g., a Hänsch-Couillaud mechanism.
  • the dual optical-frequency reference source 100 comprises a dual-mode laser source.
  • the dual optical-frequency reference source 100 comprises first and second reference laser sources that are each frequency-locked to a corresponding distinct resonant optical mode of a common optical reference cavity 180 ( Fig. 1 ).
  • the dual optical-frequency reference source 100 comprises first and second reference laser sources that are each frequency-locked to a corresponding distinct atomic transition 190 ( Fig. 1 ). Any other suitable stabilized dual optical-frequency reference source can be employed that provides needed, desired, or suitable ( i.e., operationally acceptable) reference frequencies and difference frequency stability.
  • the electro-optic sideband generator comprises only two or more electro-optic phase modulators 220/230 (path I of Fig. 2 ) each driven by a corresponding portion of the sideband generator input electrical signal at the frequency f M .
  • the two or more phase modulators 220/230 (which form the portion 200 of the sideband generator) are arranged in series so as to sequentially transmit the first and second optical reference signals 120a/120b so as to generate the multiple optical sideband signals 310 at corresponding sideband optical frequencies of the form v 1 ⁇ n t f M and v 2 ⁇ n 2 f M , wherein n 1 and n 2 are integers.
  • pairs of sideband optical signals are generated with n 1 + n 2 ranging from 2 up to at least 30.
  • the conventional technique of continuum generation is included in the portion 300 of the electro-optic sideband generator (path II of Fig. 2 ), which comprises the two or more electro-optic phase modulators 220/230, an intensity modulator 320, a dispersion compensator 330, an optical amplifier 340, and a nonlinear optical medium 350.
  • the two or more electro-optic phase modulators 220/230 are each driven by a corresponding portion of the sideband generator input electrical signal at the frequency f M , derived from the VCO output signal 620 and synchronized with phase shifters 224/234.
  • the intensity modulator is driven by another portion of the sideband generator input electrical signal at the frequency f M , derived from the VCO output signal 620 and synchronized with phase shifter 324.
  • the phase modulators 220/230, the intensity modulator 320, the dispersion compensator 330, the optical amplifier 340, and the nonlinear optical medium 350 are arranged in series so as to sequentially, in order, transmit the first and second optical reference signals so as to generate the multiple optical sideband signals 310.
  • Those signals are at corresponding frequencies of the form v 1 ⁇ n 1 f M and v 2 ⁇ n 2 f M , wherein n 1 and n 2 are integers with n 1 + n 2 ranging from 2 up to at least 100 or more.
  • the intensity modulator comprises an electro-optic Mach-Zehnder interferometer
  • the dispersion compensator 330 can comprise a suitable length of suitably dispersive optical fiber (e.g., dispersion-shifted optical fiber or an optical fiber including a dispersion-shifting grating)
  • the optical amplifier 340 can comprise an erbium-doped optical fiber amplifier (EDFA)
  • the nonlinear optical medium 350 can comprise a suitable length of highly nonlinear optical fiber (HNLF).
  • Other functionally equivalent components can be employed, e.g., an electroabsorption modulator. As suitable techniques for generating large phase amplitude modulation are developed or become available it may become possible to replace the above functions with fewer or even a single phase modulator.
  • optical frequency division now enables the generation of ultra-stable microwave-frequency signals with record low phase noise.
  • a key ingredient for OFD is a stable optical frequency reference (OFR).
  • Optical references can be of two types: an absolute frequency reference or a difference-frequency reference. The latter type of reference and is well suited for application with the optical frequency divider described herein.
  • the inventive dual-frequency optical source illustrated schematically in Figs. 7 and 8 will now be discussed in more detail.
  • the dual-frequency optical source 100 is based on THz-bandwidth dual-mode stimulated Brillouin lasers (SBLs).
  • the phase noise of the dual-mode SBL difference frequency reference is measured to be -105 dBc/Hz at 1 kHz offset when the frequency reference is set to a difference frequency directly-detectable with an optical detector (e.g., a few 10s GHz, perhaps 100 GHz). This is already an excellent phase noise level, representing a 15 dB improvement over previous Brillouin lasers.
  • an optical detector e.g., a few 10s GHz, perhaps 100 GHz.
  • This difference frequency it is desirable to increase this difference frequency to very high (i.e., not directly detectable) values greater than about 300 GHz up to about 1 THz, about 5 THz, about 10 THz, about 100 THz, or even beyond 100 THz.
  • phase noise of the dual mode SBL difference frequency is determined by the fundamental Schawlow-Townes frequency noise of the two lasers, which is approximately invariant with respect to the frequency separation between them.
  • optical frequency division such large difference frequency (not detectable using optical detectors) values can be divided down to a conventionally detectable frequency (e.g., 10s of GHz).
  • the phase noise of the difference frequency is reduced in the divided-down signal by the square of the division ratio.
  • the frequency-division-induced reduction of phase noise is predicted to enable record-low phase noise at microwave frequencies.
  • the inventive difference-frequency reference can be generated using standard fiber-optic components and requires little or no costly hardware. It should therefore be easily transferable to many different uses and applications.
  • microwave-frequency signal is directly generated by beating of the dual optical modes of the laser on the optical detector, so the generated microwave-frequency signals are limited by the bandwidth of the optical detector (up to perhaps 100 GHz).
  • phase noise of the microwave-frequency signal is equal to the phase noise of the relative frequency stability of the two laser modes.
  • inventive dual-frequency optical source 100 we transform the conventional role of the optically detected dual-mode lasers (bandwidth up to 100 GHz) to stable optical reference references, with much larger frequency separation in a range between about 300 GHz to about 100 THz or even higher.
  • the reference difference frequency produced by the inventive dual-mode stimulated Brillouin lasers (SBL) can then be divided down to microwave frequencies using optical frequency dividers (such as the inventive electro-optic frequency divider described above, or a conventional mode-locked laser frequency comb).
  • the phase noise of the generated microwave-frequency signal is also divided from that of the relative stability between the dual mode SBLs by 20log 10 N dB, where N is the division factor.
  • phase noise of the optically divided microwave-frequency signal can be greatly reduced relative to that of the dual-frequency optical-frequency reference, which as noted above has low phase noise itself.
  • Optical frequency division is a relatively new approach to microwave generation. Frequency references, both absolute or difference-based, have typically used passive Fabry-Perot resonators, which are bulky and delicate devices.
  • an inventive dual-frequency optical source 100 comprises first and second pump laser sources 130a/130b and an optical resonator 110 (a disk resonator; Fig. 7 ) or 110' (a fiber-loop resonator; Fig. 8 ).
  • the first and second pump laser sources arranged to generate optical pump power at respective first and second pump laser frequencies v pump1 and v pump2 , corresponding to respective first and second pump wavelengths ⁇ pump1 and ⁇ pump2 .
  • the optical pump power is routed into the optical resonator 110/110' using a circulator 114; other suitable arrangements can be employed, e.g., a beamsplitter.
  • the optical resonator 110/110' is characterized by a Brillouin shift frequency v B and a free spectral range (FSR) that is substantially equal to an integer submultiple of the Brillouin shift frequency.
  • FSR free spectral range
  • Each one of the first and second pump laser sources 130a/130b is frequency-locked to a corresponding resonant optical mode of the optical resonator 110/110'; any needed, desired, or suitable frequency-locking technique or mechanism can be employed.
  • the output signals 120a/120b are routed out of the dual-frequency source 100 using a circulator 114; other suitable arrangements can be employed, e.g., a beamsplitter or a fiber coupler.
  • the dual-frequency optical source 100 is arranged and operated so that the output difference frequency v 2 -v 1 is greater than about 300 GHz.
  • the output difference frequency v 2 -v 1 is greater than about 1 THz; in some examples the output difference frequency v 2 -v 1 is greater than about 5 THz; in some examples the output difference frequency v 2 -v 1 is greater than about 10 THz; in some of those examples the output difference frequency v 2 -v 1 is greater than about 100 THz. Because the frequencies v 1 and v 2 are generated within the same cavity, there is high degree of correlation in their respective fluctuations so that the difference frequency v 2 -v 1 is quite stable. Also, other resonator geometries (e.g., a linear resonator) can be employed for generating the dual SBL reference lines.
  • a method for generating first and second optical output signals 120a/120b comprises simultaneously pumping the optical resonator 110/110' with optical pump power from first and second pump laser sources 130a/130b.
  • the free spectral range (FSR) of the optical resonator 110/110' is substantially equal to the Brillouin shift frequency of the optical resonator.
  • the optical resonator comprises silica and the Brillouin shift frequency of the optical resonator is about 10.9 GHz; other needed, desired, or suitable materials can be employed that exhibit different Brillouin shift frequencies.
  • the reference optical signals 120a/120b can be provided at any needed, desired, or suitable optical frequencies.
  • first and second optical reference frequencies v 1 and v 2 are each between about 75 THz and about 750 THz (i.e., wavelengths between about 400 nm and about 4 ⁇ m), between about 120 THz and about 430 THz ( i.e., wavelengths between about 700 nm and about 2.5 ⁇ m), or between about 150 THz and about 300 THz ( i.e., between about 1 ⁇ m and about 2 ⁇ m).
  • the latter two ranges can be convenient due to ready availability of fiber-optic and/or solid state sources in those wavelength regions.
  • Other wavelengths can be employed.
  • the dual optical-frequency reference source 100 is stabilized so as to maintain fluctuations of a reference difference frequency v 2 -v 1 (i.e., relative frequency stability of the lasers) within an operationally acceptable optical reference bandwidth.
  • the operationally acceptable reference bandwidth (given as a bandwidth characterized over a given time interval) is less than about 100 Hz over about a 1 second timescale, or less than about 1 Hz over about a 1 second timescale.
  • the operationally acceptable reference bandwidth (given as optical phase noise at a given offset frequency relative to the optical carrier frequency) is about -40dBc/Hz at 100Hz offset frequency and about -80dBc/Hz at 10kHz offset frequency, or about -80dBc/Hz at 100Hz offset frequency and about -125 dBc/Hz at 10kHz offset frequency.
  • improved levels of relative stability of the laser sources will translate directly into improvements in the overall frequency stability of the microwave-frequency output signal.
  • Still better stabilized references can be employed as needed, desired, or suitable, or as suitable optical sources are developed or become available.
  • each one of the first and second pump laser sources is frequency-locked to the corresponding resonant optical mode of the resonator 110/110' by a Pound-Drever-Hall mechanism; any suitable mechanism can be employed, e.g., a Hänsch-Couillaud mechanism.
  • a Hänsch-Couillaud mechanism e.g., a Hänsch-Couillaud mechanism.
  • each pump laser 130a/130b (emitting at corresponding wavelengths ⁇ 1 and ⁇ 2 ) is frequency-locked to a corresponding distinct resonant optical mode of the disk resonator 110 using the Pound-Drever-Hall (PDH) technique, is coupled into the disk resonator 110 by a circulator 114, and excites its own corresponding Brillouin laser in the backward-propagating direction at respective optical reference frequencies v 1 and v 2 .
  • PDH Pound-Drever-Hall
  • the PDH technique is implemented for each pump laser 130a/130b by employing respective optical bandpass filters 132a/132b, photodetectors 134a/134b, and feedback/servo mechanisms 136a/136b; control of each pump wavelength can be via direct laser control (as with pump laser 130a) or via frequency shifting of the laser output (as with acousto-optic shifting of the output of pump laser 130b).
  • the frequency separation i.e., the difference frequency v 2 - v 1
  • the frequency separation i.e., the difference frequency v 2 - v 1
  • FIG. 8 shows a similar example wherein the disk resonator 110 has been replaced by a fiber-loop optical resonator 110' (i.e., a fiber-loop cavity or FLC), and wherein both pump lasers 130a/130b are subject to direct control of their respective wavelengths.
  • a fiber-loop optical resonator 110' i.e., a fiber-loop cavity or FLC
  • a fiber-loop optical resonator 110' enables use of readily available fiber optic components that have been developed for telecommunications-related applications, and also enables a performance benefit in terms of a significantly lower phase noise (up to 40 dB lower) in the frequency reference itself compared with the disk resonator 110. This improvement is believed to arise for two reasons. First, the fiber-loop cavity has a much larger round trip length (on the order of 100m to 500m) compared with a disk resonator (round trip length on the order of 10 mm to 100mm). Consequently, frequency fluctuation arising from random temperature fluctuations of the fiber loop cavity are greatly reduced relative to the disk resonator.
  • the longer cavity length of a fiber-loop cavity results in a correspondingly longer intracavity photon storage time compared to the disk resonator.
  • a longer photon storage time in turn leads to correspondingly lower fundamental Schawlow-Townes frequency noise of the laser.
  • dual-pumped Brillouin lasers using optical fiber have been previously demonstrated (as noted above), they have been operated as microwave sources with frequency separation typically less than about 100 GHz and not as difference frequency references with frequency separation greater than about 300 GHz, about 1 THz, about 5 THz, about 10 THz, about 100 THz, or even higher.
  • difference frequency references with frequency separation greater than about 300 GHz, about 1 THz, about 5 THz, about 10 THz, about 100 THz, or even higher.
  • optical frequency division techniques disclosed above there would have been no need to generate dual reference frequencies so widely spaced apart. There also has been no attempt to characterize or to understand operation of the dual-Brillouin laser with this application in mind.
  • Figs. 7 using a disk resonator 110
  • Fig. 8 using a fiber-loop resonator.
  • two pump lasers 130a/130b are frequency-locked to the Brillouin-active fiber loop cavity 110' (FLC) using the standard Pound-Drever-Hall locking technique employing optical bandpass filters 132a/132b, photodetectors 134a/134b, and feedback/servo mechanisms 136a/136b.
  • Each pump laser 130a/130b excites its own stimulated Brillouin laser once the circulating pump power in the fiber-loop cavity 110' reaches threshold.
  • the frequency separation between the two SBLs can be tuned from 10s of MHz to 100 THz or more by tuning the frequency separation between the two pump lasers 130a/130b.
  • frequency separation between the two SBLs can be on the order of several THz. For example, using one pump laser at 1550nm, the frequency separation of the two SBLs can be set to 1 THz (tuning the second pump laser to 1542nm), to 10 THz (tuning the second pump laser to 1473nm), or to 100 THz (tuning the second pump laser to 1022nm).
  • the difference frequency between the co-oscillating, dual-mode SBL outputs is then used as the stable optical-frequency reference in the frequency division process (as in Fig. 3 ).
  • Any suitable optical divider can be employed, including in some examples the electro-optic frequency divider described above.
  • the OFD is based on the conventional mode-locked optical frequency comb (OFC), where two comb lines of the OFC are frequency-locked to the two SBLs such that the repetition rate of the OFC gives a stable, divided microwave output.
  • OFC optical frequency comb
  • the inventive electro-optic frequency divider is simpler to implement and has been observed to relax the linearity constraints of high-bandwidth photodetection that have posed significant challenges for optical frequency division based on mode-locked OFC.
  • a series of FLCs have been constructed, consisting of a 90/10 fused coupler, and different cavity round trip path lengths of 45 meter (FSR 4.4 MHz), 200 meter (FSR 1 MHz) and 500 meter (FSR 400 kHz); any other needed, desired, or suitable fiber-loop cavity length can be employed, .e.g., greater than or equal to about 40 meters long, greater than or equal to about 100 meters long, greater than or equal to about 200 meters long, or greater than or equal to about 500 meters long.
  • a longer fiber-loop optical resonator typically exhibits less frequency and phase noise relative to a shorter fiber-loop optical resonator, all other things being equal.
  • the measured optical finesse of these FLCs are around 40 (mainly limited by the coupler loss), and the pump threshold for SBS oscillation is on the order of a few hundred microwatts. Above SBL threshold, the pump power of each pump laser (at 1550nm wavelength region) is increased until a point is reached ( ⁇ 1 mW) such that lasing at the first-order Stokes frequency starts to excite second-order Stokes waves in the resonator.
  • Fig. 9B shows the measured optical spectrum of the dual-mode SBL difference frequency reference with a frequency separation of 1.61 THz (12.5 nm), obtained by dual pumping the FLC at 1537.2 nm and 1549.6 nm.
  • the frequency separation of the dual SBLs is tuned to a frequency sufficiently low to be detected directly using a fast photodiode and processed electronically (this is essentially the case of unity division).
  • the detected beat note is set at 20 GHz and its phase noise is measured using a phase noise analyzer (Rohde Schwartz, model number FSUP26).
  • the measured single-sideband (SSB) phase noise spectra of the SBL beat note from the different FLCs are shown in Fig. 9A (45m FLC: top solid curve; 200m FLC: middle solid curve; 500m FLC: bottom solid curve).
  • phase noise spectra show a Schawlow-Townes-noise-limited phase noise (1/ f 2 dependence) over a broad range of offset frequencies starting from a few Hz to over 100 kHz.
  • the common-mode technical noise of the SBLs substantially cancels out of the beat note signal upon optical detection.
  • the phase noise of the relative frequency stability in the dual mode SBLs is limited by the fundamental Schawlow-Townes noise and is invariant with the frequency separation between the two co-oscillating SBLs. Therefore, with the dual-mode SBLs tuned to larger difference frequency, a significant reduction in phase noise results from the optical frequency division process.
  • the optically-divided microwave-frequency signal ( f M ) benefits from the reduction of the optical phase noise by the square of the division ratio, N ⁇ ( v 2 -v 1 )/ f M .
  • N the division ratio
  • the measured single-side-band (SSB) phase noise of the difference frequency of the dual-mode SBLs (without any optical frequency division) is already improved compared with previous results.
  • the measured phase noise of the dual-mode SBL beat note (carrier: 20 GHz, offset frequency: 1 kHz) is -95 dBc/Hz (45m FLC), -101 dBc/Hz (200m FLC), and -105 dBc/Hz (500m FLC), as shown in Fig. 9A .
  • the 500m FLC exhibited about -125 dBc/Hz at 10 kHz offset frequency, compared to about -83 dBc/Hz for a disk resonator with a roundtrip length of about 18 mm.
  • the predicted phase noise of the optically-divided microwave signals based on OFD from the dual-mode SBL difference frequency reference is also plotted in Fig. 9A .
  • the carrier frequency of the optically divided microwave signal is fixed at 10 GHz. Therefore, these division ratios correspond to the dual-mode SBL frequency separation set to 330 GHz, 1 THz, and 3.3 THz respectively.
  • the predicted phase noise levels in Fig. 9A represent record low levels.
  • the oscillator based on the SBL difference frequency reference does not require costly hardware, nor does it need to operate at vacuum or cryogenic conditions.
  • the technology can be easily deployed in various applications, such as radar, communications, and navigation systems.

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